Off-critical Luttinger Junctions

TL;DR

This paper studies off-critical Luttinger junctions of quantum wires, analyzing how bound and antibound states in the scattering matrix influence the system's equilibrium and non-equilibrium properties, including conductance.

Contribution

It provides a detailed analysis of how bound states affect the physical regimes and conductance in off-critical Luttinger junctions, extending understanding beyond critical points.

Findings

Bound states lead to non-equilibrium energy flows.

Scattering matrix without bound states corresponds to equilibrium.

Explicit conductance tensor formulas for both regimes.

Abstract

We investigate Luttinger junctions of quantum wires away from criticality. The one-body scattering matrix, corresponding to the off-critical boundary conditions at the junction, admits in general antibound and/or bound states. Their contribution to the theory is fixed by causality. The presence/absence of bound states determines the existence of two different regimes with inequivalent physical properties. A scattering matrix without bound states defines an isolated equilibrium system. Bound states instead drive the system away from equilibrium, giving raise to non-trivial incoming or outgoing energy flows in the junction. We derive in both regimes and in explicit form the electromagnetic conductance tensor, pointing out the different impact of bound and antibound states.